Wow, I think you've nailed it! After reading your post, I started digging into that and came across this, discussing this exact issue:

I'm posting the modified code here so as not to make the OP confusing. The new code no longer closes the connection immediately, but the timer, for some reason only fires ONCE (the first time), whereas I would like it to keep going. I'm guessing this has something to do with the line undef $w; but when I get rid of it, the timer doesn't fire at all.

#!/usr/bin/perl

use strict;
use warnings;

use Plack::Builder;
use SockJS;
use AnyEvent;

builder {
    mount '/echo' => SockJS->new(
        handler => sub {
            my ($session) = @_;

            $session->on(
                'data' => sub {
                    my $session = shift;

                    $session->write('got your message');
                }
            );

            $session->write('connected');

            my $w_cond = AnyEvent->condvar;
            $w_cond->cb( sub { warn $_[0]->recv } );
            my $w; $w = AnyEvent->timer(
                after => 0,
                interval => 5,
                cb => sub {
                    undef $w; # cleanup
                    $session->write('5 seconds have passed');
                    $w_cond->send();
                }
            );
        };
    );
};
[download]